A heterogeneous Bertrand duopoly game with bounded rational and adaptive players manufacturing differentiated products is subject of investigation. The main goal is to demonstrate that participation of one bounded rational player in the game suffices to destabilize the duopoly. The game is modelled with a system of two difference equations. Evolution of prices over time is obtained by iteration of a two dimensional nonlinear map. Equilibria are found and local stability properties thereof are analyzed. Complex behavior of the system is examined by means of numerical simulations. Region of stability of the Nash equilibrium is demonstrated in the plane of the speeds of adjustment. Period doubling route to chaos is presented on the bifurcation diagrams and on the largest Lyapunov characteristic exponent graph. Lyapunov time is calculated. Chaotic attractors are depicted and their fractal dimensions are computed. Sensitive dependence on initial conditions is evidenced.

The integration of chaos theory and history has been an issue ofmany scientific discussions, but failed to produce any results. Author reexamines the discussions, mathematical features of the theory and claims that proposed ways of integration couldn't have been used practically. Author asks if such integration is possible and i fit can have any intrinsic value for advancement of historical knowledge. Proposed solution is to use chaos theory as a tool, which enables historians to analyze causal relations in the past.

Double-beam model is considered in many investigations both theoretical and typically engineering ones. One can find different studies concerning analysis of such structures behaviour, especially in the cases where the system is subjected to dynamic excitations. This kind of model is successfully considered as a reliable representation of railway track. Inclusion of nonlinear physical and geometrical properties of rail track components has been justified by various computational studies and theoretical analyses. In order to properly describe behaviour of real structures their nonlinear properties cannot be omitted. Therefore a necessity to search appropriate analytical nonlinear models is recognized and highlighted in published literature. This paper presents essential extension of previously carried out double-beam system analysis. Two nonlinear factors are taken into account and parametrical analysis of the semi-analytical solution is undertaken with special emphasis on different range of parameters describing nonlinear stiffness of foundation and layer between beams. This study is extended by preliminary discussion regarding the dynamic effects produced by a series of loads moving along the upper beam. A new solution for the case of several forces acting on the upper beam with different frequencies of their variations in time is presented and briefly discussed.

The chaotic phenomena of coronary artery systems are hazardous to health and may induce illness development. From the perspective of engineering, the potential harm can be eliminated by synchronizing chaotic coronary artery systems with a normal one. This paper investigates the chaos synchronization problem in light of the methodology of sliding mode control (SMC). Firstly, the nonlinear dynamics of coronary artery systems are presented. Since the coronary artery systems suffer from uncertainties, the technique of derivative-integral terminal SMC is employed to achieve the chaos synchronization task. The stability of such a control system is proven in the sense of Lyapunov. To verify the feasibility and effectiveness of the proposed method, some simulation results are illustrated in comparison with a benchmark.

Many nonlinear dynamical systems can present a challenge for the stability analysis in particular the estimation of the region of attraction of an equilibrium point. The usual method is based on Lyapunov techniques. For the validity of the analysis it should be supposed that the initial conditions lie in the domain of attraction. In this paper, we investigate such problem for a class of dynamical systems where the origin is not necessarily an equilibrium point. In this case, a small compact neighborhood of the origin can be estimated as an attractor for the system. We give a method to estimate the basin of attraction based on the construction of a suitable Lyapunov function. Furthermore, an application to Lorenz system is given to verify the effectiveness of the proposed method.

Electromagnetic mill installation for dry grinding represents a complex dynamical system that requires specially designed control system. The paper presents model-based predictive control which locates closed loop poles in arbitrary places. The controller performs as gain scheduling prototype where nonlinear model – artificial recurrent neural network, is parameterized with additional measurements and serves as a basis for local linear approximation. Application of such a concept to control electromagnetic mill load allows for stable performance of the installation and assures fulfilment of the product quality as well as the optimization of the energy consumption.

In this paper, a model of an electromagnetic system with two levitating magnets is presented. Modeling was performed using the results of experiments. The data obtained make it possible to fit the magnetic forces between two magnets using a 5th order polynomial. The time series show that dry friction constitutes an important part of damping forces. The differential equations of motion consider strong nonlinearities of magnetic and damping forces. These terms cause the nonlinear hardening effect. The energy recovered by magnetic induction is dissipated in the resistors. Numerical simulations show that resistance has an impact on magnet dynamics and energy recovery. From the resonance characteristics obtained, optimal resistance is determined when energy recovery is the highest.

Although the study of oscillatory motion has a long history, going back four centuries, it is still an active subject of scientific research. In this review paper prospective research directions in the field of mechanical vibrations were pointed out. Four groups of important issues in which advanced research is conducted were discussed. The first are energy harvester devices, thanks to which we can obtain or save significant amounts of energy, and thus reduce the amount of greenhouse gases. The next discussed issue helps in the design of structures using vibrations and describes the algorithms that allow to identify and search for optimal parameters for the devices being developed. The next section describes vibration in multi-body systems and modal analysis, which are key to understanding the phenomena in vibrating machines. The last part describes the properties of granulated materials from which modern, intelligent vacuum-packed particles are made. They are used, for example, as intelligent vibration damping devices.

The longitudinal automatic carrier landing system (ACLS) control law is designed based on nonlinear dynamic inversion (NDI), which can reject air wake, decouple lateral states, and track the dynamic desired touchdown point (DTP). First of all, the nonlinear landing model of F/A−18 aircraft in the final approach is established, in which the parameters of the aerodynamic, control surfaces, and limited states are acquired. Second, the strategy of tracking the desired longitudinal trajectory through pitch angle control is adopted. The automatic power compensation system (APCS), pitch angle rate, pitch angle, and vertical position control loops are developed based on the adaptive NDI. The stable analysis and the principal description are derived in detail. Deck motion compensation (DMC) algorithm is designed by frequency response method. Third, the control parameters are optimized through the genetic algorithm. A fitness function integrated with velocity, angle of attack (AOA), pitch rate, pitch angle, and vertical position of the aircraft are proposed. Finally, integrated simulations are conducted on a semi-physical simulation platform. The results indicate that the adopted automatic landing control law can achieve both excellent performance and the ability to reject the air wake and lateral coupling.

Management and Production Engineering Review (MPER) is a peer-refereed, international, multidisciplinary journal covering a broad spectrum of topics in production engineering and management. Production engineering is a currently developing stream of science encompassing planning, design, implementation and management of production and logistic systems. Orientation towards human resources factor differentiates production engineering from other technical disciplines. The journal aims to advance the theoretical and applied knowledge of this rapidly evolving field, with a special focus on production management, organisation of production processes, management of production knowledge, computer integrated management of production flow, enterprise effectiveness, maintainability and sustainable manufacturing, productivity and organisation, forecasting, modelling and simulation, decision making systems, project management, innovation management and technology transfer, quality engineering and safety at work, supply chain optimization and logistics. Management and Production Engineering Review is published under the auspices of the Polish Academy of Sciences Committee on Production Engineering and Polish Association for Production Management. The main purpose of Management and Production Engineering Review is to publish the results of cutting-edge research advancing the concepts, theories and implementation of novel solutions in modern manufacturing. Papers presenting original research results related to production engineering and management education are also welcomed. We welcome original papers written in English. The Journal also publishes technical briefs, discussions of previously published papers, book reviews, and editorials. Letters to the Editor-in-Chief are highly encouraged.